> On 12 Dez., 00:43, Virgil <vir...@ligriv.com> wrote:> > > > That is potential infinity. There is no set of natural numbers that is> > > larger than every FISON.> >> > While there is no set of natural numbers larger than every SET of> > fisons, there is a set of natural numbers larger than any single fison,> > This is impossible, because all natural numbers belong to a single> FISON by definition of the inclusion monotonic set of FISONs obtained> from the set of exponents of the sequence (a_k) with a_k = 10^-1 +> 10^-2 + ... + 10^-k.

The objects of that definition coincides with the John von Newumann naturals, which collectively form an actually infinite set in ZFC.

I.e., it is a set allowing injection to a proper subset.

For example, the mapping n -> n+1 maps the set of all JvN naturals to a proper subset of the set of all JvN naturals.

Or does WM claim to be able to find some n for which there does not exist any n+1?--